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Q: ®. *,(t)=l, tilt)=t, Xglt) =t² Let [oD. Use Gran-Schridlt on er thogonolize e, 2) process to

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Q: Find ôz|ðu and ôzlôv for z=4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4).

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Q: Calculate fls f(æ, y, z) dS For 2² + y² = 16, 0 < z S ls f(x, y, z) dS =

A: Introduction: The surface integral is used in mathematics to add a collection of values associated…

Q: Find a. Əw dx a. aw əx and b. y (2π,1,-π) Əw at the point (x,y,z) = (2π, 1₁ - π) if w = x² + y² + z²…

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Q: Q, Determine the PDF for multiple RV Y (a) Y, = X,tXz+ X3 Con dition Xi,Xz, X3 are wni formly…

A: Let us consider Irwin-Hall distribution as follows: Let X1, X2, ...., Xn be a random sample of size…

Q: If u=x2y+y2z+z2x then show that du/dx + du/dy + du/dz = (x+y+z)2

A: Given u=x2y+y2z+z2x. Find dudx as follows.…

Q: Evaluate S S f3zdV where E is the solid enclosed by z = 1 and z = x2 +y?

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Q: 4. Which would not be sufficient to prove AWXZ AWYX? C ZWXZ = LY WZ А WX XW YW WZ D WX WX XY XZ WX…

A: To show that the given two triangles are similar we need to show that the sides of the two triangles…

Q: z = x* + xy", x = uv* + w², y= u +ve" dz when u = dv Find 3, v = 1, w = 0

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Q: OW Let w = f(x, y, z) and let x =psinocos0 and y = psinosin0 and z = pcoso. Find

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Q: Let M and m be the maximum and minimum values of Ax, y) = 5x + 4y on the region x +y < 49 . Then…

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Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: . Solve the following problem with insulated boundaries: Uz = Uxx Ju,(0, t) = 0 lu(1, t) = 0 u(x, 0)…

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Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: If z=sin(x^2+y^2),x=vcos(u),y=vsin(u) find ∂z/∂u and ∂z/∂v.   ∂z/∂u= ∂z/∂v=

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Q: Under a change of variables z = u°/3, y = v²/2 , the infinitesimal element of area dædy becomes 6uv…

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Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: ve the given boundary-value problem. (If an answer does not exist, enter DNE.) y" + y = 0, y'(0) =…

A: Topic:- differential equations

Q: Let ry w = and a = 2s + t, y = st, z = 2s - t dw dw Find ds' at

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Q: Integrate f(x,y,z) = x+ Vy -z° over the path from (0,0,0) to (3,9,3) given by C,: r(t) =t i+tj,…

A: The given function is, Let, Also the given paths are, So,

Q: and y have density flay)=82y tor Find ECX14) and ECYIX) リフズ7679 %3D

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Q: f (x, y, z) is continuous on the rectangular box B = [a, b] × [c, d] × [m, n], then Sm S" Sa f (x,…

A: Triple integral in Rectangular Box :  If f(x,y,z) is continuous on a rectangular box B=…

Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1

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Q: Q1: - Find Ow/Du and Əw/Əv if w- xy + yz + xz ,x-utv, yru-v,z-uv at the point (u,v)- (0.5,1) (30…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let v f(x,y) and w f(x, y). Choose a correct formula %3! to determine where J is a Jacobian. dv aw…

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Q: Given w = In(") + 8z*y* /z find %3D mmadı zerinden mmis xy + 12.x ayu Ob. 72x y 12E +96x'y Od.…

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Q: Evaluate S S12zdV E where E is the solid enclosed by z = 1 and z = x² + y² 2. Immmmm

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Q: Eraluate: 1. JJR e-(n^²+yv) the eincles of padii 1& 2 dady, R is the region of between.

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: Evaluate       C(2x − y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

A: We have to evaluate the integral ∫2x-ydx+x+3ydy along the path C, where C:y=x52 from 0,0 to 4,32.

Q: Let f(x,y) = xsin(xy), then fx(x,y) = O sin(xy) + x²cos(xy) O x²cos(xy) O sin(xy) + xycos(xy)…

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Q: Find the defivativesof y o x with resPect Ysxě_eX

A: To find the derivative

Q: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: The shaded area shown in (Figure 1) is bounded by y axis and the curve y? = (1.44 – x) m, where z is…

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Q: j ula,0) =f(2) solue (4 Us ing neumann Boundary Conditions o lg Periodic Boundary conditio, usile

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Q: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

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Q: If V V30 everywhere then the resuiting flow is c O rotational O dynamic Osteady Pirrotational

A: The general form of a vector-valued function in three dimensions is given by F→=F1i^+F2j^+F3k^,…

Q: O Given the initicl bouridary conditions y(0) =0, y'c0) = 1, letrmine the, solntiem of %3D…

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Q: Calculate (y+z)dx+ (x+ z)dy+ (x+y)dz , where C consists of line segments from (0,0,0) to (3,2,4) and…

A: We will use parametric equation of lines to find the integral

Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: . Given: WZ 1 ZY; WX 1 XY; WX = YZ Prove: Wz || XY Y W

A: Since, we have been given that WZ ⊥ ZY , WX ⊥ XY and WX ≅ XYOur Aim is to prove that WZ  ∥ XY

Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…

A: We have to find x

Q: Obtain the DE of the family of lines passing through (2,0). Select one: о 2ydar — (z — 1)dy o (x –…

A: We find the differential equation of the family lines passing through (2 , 0)

Q: . SS, xcos(y)dA, D is bounded by y = 0,y = x² ,x = 1.

A: See the details solution in below

Q: 3. Given that p, = x + xy, calculate f,p, dS over the region y sx", 0 < x < 1.

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Q: 17. Let AXYZ be circumscribed on O R, and let XS = 5, SY = 32, and YZ = 64.* *Image not set to…

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Q: 2. Given: CE bisects 4FCD and CF = CD Prove: ZF ZD 1. CE bisects < FCD 1. 2. 2. Given 3. 3. Def of…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.